Mirror images can be explained by geometrical optics, assuming that light is made up of rays. It is not made up of rays, but the method works.
Some mirrors magnify their images, and reflecting telescopes use surface-silvered magnifying mirrors as well as lenses, to produce clear images.
Images from flat mirrors reverse left and right, but curved mirrors reflect differently, depending on the curvature and the distances of object and viewer.
Around 1000, Alhazen studied lenses and their operation in Cairo, tried to puzzle out where the colours of the rainbow come from, and used a camera obscura.
Around 1250, Roger Bacon studied the use of lenses to assist the vision, and he may even have found the principle of combining different lenses in a telescope.
In 1621, Willebrod Snell published his law of refraction, which related the sines of the angles of incidence and refraction, known today simply as Snell's law.
In 1637, René Descartes used Snell's law about the bending of rays passing in and out of glass to explain fully the operations of concave and convex lenses.
One effect of light slowing down is that it bends in a mathematically predictable way. This is called refraction, and refracted light obeys Snell's law.
Any transparent material has a refractive index that can be measured. This value can then be used to predict how that material will refract light.
Lenses and prisms depend on the bending of light in the process of refraction. Prisms can bend or reflect light internally, depending on the angle of incidence.
Imperfect images from lenses may be caused by spherical aberration. Spherical aberration can be reduced by using a smaller aperture for viewing an object.
We see more clearly with a bright light, because the iris of our eye closes to give a smaller aperture, as a smaller aperture gives a greater depth of field.
Imperfect images with coloured fringes may be caused by chromatic aberration in lenses. Chromatic aberration may be kept under control with an achromatic lens.
Lenses can be used to focus rays so that they converge at what is called the focal point. This is why lenses can be used to form and project an image.